Figure 2. Simulations of the dynamics faithfully reproduce neuronal activity and behavioral statistics.

(A) Experimentally observed (top) and simulated (bottom) activity of 15 shared neurons plotted as in Figure 1A. (B) Trace of the simulated AVA neuron colored according to the inferred behavioral state. In contrast to Figure 1, color here expresses neuronal activity as z-score computed for each neuron individually. Behavioral states are assigned based on experimentally observed distribution of behaviors for each point in phase space (blue $\mathrm{\to }$ forward locomotion; green $\mathrm{\to }$ backward locomotion) (Materials and methods). Both A and B are plotted on the same time-axes. Because of under-sampling, transitions between forward and backward locomotions are left unassigned (gray). (C) Dwell time distributions for forward locomotion, backward locomotion and backing bouts (blue $\mathrm{\to }$ experimentally observed; orange $\mathrm{\to }$ simulated). Backing bouts were defined as repeated episodes of backing behavior separated by short forward locomotion states lasting at most 30 frames ( 10 s) (e.g. black line in B). Although the manifold is constructed on the basis of transition probabilities between states separated by <1 s., the manifold successfully predicts statistics of behaviors over 100 s.

Figure 2—figure supplement 1. Neuronal activity trace spectral residues.

Each line gives the difference in fractional power of the spectrum of the observed neuron and it’s simulated partner. The simulated and observed spectra are in good agreement for all frequencies above 0.05 Hz (where finite data artifacts are most prevalent).

Figure 2—figure supplement 2. Auto correlations and auto mutual information inform expected delay time scales.

The auto correlation (A) and auto mutual information (B) for the experimentally observed neuronal activation in the (Kato et al., 2015) dataset (blue boxes), along with the auto correlation and auto mutual information of their derivatives (red boxes) is plotted for time lags up to 100 s. In the article, we used autocorrelations to estimate an appropriate choice of $\tau$. We selected a delay time based on the minimum (across neurons) auto correlation time constant (10 frames, 4 s). Choice of $\tau$ is not trivial for a multivariate system. However, the results do not strongly depend on this choice so long as the total delay time is ∼ 50 frames (∼ 18 s) Figure 2—figure supplement 3.

Figure 2—figure supplement 3. Effect of delay embedding parameters on model accuracy.

The delay embedding parameters (number of delays and delay length) are varied to test for robustness. Dots represent a unique pair of parameters. For each pair the method is rerun on all 15 neurons from all five animals in the Kato et al. (2015) dataset and the accuracy of this new model’s simulated motor command dwell time distributions are compared to the observed distributions. Color represents the relative information compared to the original model. Relative information of 1 means that the model constructed using a particular set of delay lengths and number of delays performed as well as the parameter values used in the manuscript (red diamond) (Materials and methods). Note that as long as the total delay length is about 50 time steps the model tends to perform well (about 60% of the original model’s performance).

Figure 2—figure supplement 4. Model can be constructed on the basis of a single neuron.

The method is applied to data from a single neuron and used to build the dwell times of motor commands as in Figure 3. Relative information of 1 means that the model constructed on a single neuron performed the same as the model based on all 15 neurons (Materials and methods). Note that AVAL, AVER and RIML approximate performance obtained when all 15 neurons are used.